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This sequence is interesting as a less constrained form of A261656, or as a 3-prime-factored form of A261658.

Unlike A261656, this sequence has many examples of the b and c of one member being the a and b of another. Two such members of this sequence are 3333=3*11*101 and 13799731 = 11*101*12421. This lets us consider a four factor composite number using both, giving 3*11*101*12421 = 41399193. The sequence of four-factor composites such as this is A261658.

It would be nice to know if, in general, analogous n-factor composites exist.

The prime factors of 795 are 3, 5, and 53. 3^4=81, 5^2=25, and the average of 81 and 25 gives 53. Thus, 795 is a member.

The prime factors of 3333 are 3, 11, and 101. 3^4=81, 11^2=121, and the average of 81 and 121 gives 101. Thus, 3333 is a member.

MAPLE

n := 20: L := []: for a from 3 to n do if isprime(a) then for b from a to n^2 do if isprime(b) then c := (a^4+b^2)*(1/2); if isprime(c) then L := [op(L), a*b*c] end if end if end do end if end do; L := sort(L): L := remove(proc (t) options operator, arrow; (3/2)*n^2*(n^4+9) < t end proc, L)